MPWR is an R package for multivariate time series (or multivariate structured longitudinal data) modeling and optimal segmentation via multiple polynomial piecewise regression (MPWR). It uses MLE for the estimation of the regression parameters with dynamic programming for the segmentation.
You can install the MPWR package from GitHub with:
# install.packages("devtools")
devtools::install_github("fchamroukhi/MPWR_r")To build vignettes for examples of usage, type the command below instead:
# install.packages("devtools")
devtools::install_github("fchamroukhi/MPWR_r",
build_opts = c("--no-resave-data", "--no-manual"),
build_vignettes = TRUE)Use the following command to display vignettes:
browseVignettes("MPWR")library(MPWR)# Application to a toy data set
data("toydataset")
x <- toydataset$x
Y <- as.matrix(toydataset[,c("y1", "y2", "y3")])
K <- 5 # Number of segments
p <- 3 # Polynomial degree
mpwr <- fitMPWR(X = x, Y = Y, K, p)
mpwr$summary()
#> ---------------------
#> Fitted MPWR model
#> ---------------------
#>
#> MPWR model with K = 5 components:
#>
#> Clustering table (Number of observations in each regimes):
#>
#> 1 2 3 4 5
#> 100 120 200 100 150
#>
#>
#> -----------------
#> Regime 1 (k = 1):
#>
#> Regression coefficients:
#>
#> Beta(d = 1) Beta(d = 2) Beta(d = 3)
#> 1 0.4474133 0.8114824 -2.368242
#> X^1 -25.5727846 -20.6848653 32.839138
#> X^2 414.9354880 499.4546427 -542.866462
#> X^3 -1816.2465442 -2484.0611667 2530.294227
#>
#> Covariance matrix:
#>
#> 1.17712603 0.11140579 0.07303982
#> 0.11140579 0.83941499 -0.02442203
#> 0.07303982 -0.02442203 0.85240344
#> -----------------
#> Regime 2 (k = 2):
#>
#> Regression coefficients:
#>
#> Beta(d = 1) Beta(d = 2) Beta(d = 3)
#> 1 21.31547 -4.118748 1.825731
#> X^1 -200.04396 113.095142 112.426768
#> X^2 906.36271 -450.243018 -494.653402
#> X^3 -1317.46869 582.074591 695.919633
#>
#> Covariance matrix:
#>
#> 1.0409636 -0.180846997 0.137540408
#> -0.1808470 1.042158071 0.009681258
#> 0.1375404 0.009681258 0.754132443
#> -----------------
#> Regime 3 (k = 3):
#>
#> Regression coefficients:
#>
#> Beta(d = 1) Beta(d = 2) Beta(d = 3)
#> 1 4.4706669 9.345977 6.347632
#> X^1 0.7561632 -33.293454 17.850830
#> X^2 -11.9495386 96.685185 -51.113538
#> X^3 16.1700162 -85.921079 42.778071
#>
#> Covariance matrix:
#>
#> 1.02025455 -0.04094228 -0.02545433
#> -0.04094228 1.15658047 0.02852561
#> -0.02545433 0.02852561 0.99749546
#> -----------------
#> Regime 4 (k = 4):
#>
#> Regression coefficients:
#>
#> Beta(d = 1) Beta(d = 2) Beta(d = 3)
#> 1 1292.041 -856.9321 -10.35385
#> X^1 -5565.070 3684.2135 19.29967
#> X^2 7964.811 -5284.7369 14.51726
#> X^3 -3790.640 2523.4936 -29.61968
#>
#> Covariance matrix:
#>
#> 0.82213717 0.00680642 -0.03667013
#> 0.00680642 1.09334196 -0.07477891
#> -0.03667013 -0.07477891 0.85425249
#> -----------------
#> Regime 5 (k = 5):
#>
#> Regression coefficients:
#>
#> Beta(d = 1) Beta(d = 2) Beta(d = 3)
#> 1 195.1972 12.91435 484.847
#> X^1 -659.8533 -45.84299 -1638.373
#> X^2 754.6710 62.05059 1862.017
#> X^3 -286.6935 -27.42044 -704.355
#>
#> Covariance matrix:
#>
#> 1.12827279 0.25684915 0.02034986
#> 0.25684915 1.21055926 0.04414336
#> 0.02034986 0.04414336 0.77644287
mpwr$plot()
# Application to a real data set (human activity recogntion data)
data("realdataset")
x <- realdataset$x
Y <- as.matrix(realdataset[,c("y1", "y2", "y3")])
K <- 5 # Number of segments
p <- 3 # Polynomial degree
mpwr <- fitMPWR(X = x, Y = Y, K, p)
mpwr$summary()
#> ---------------------
#> Fitted MPWR model
#> ---------------------
#>
#> MPWR model with K = 5 components:
#>
#> Clustering table (Number of observations in each regimes):
#>
#> 1 2 3 4 5
#> 343 335 667 423 485
#>
#>
#> -----------------
#> Regime 1 (k = 1):
#>
#> Regression coefficients:
#>
#> Beta(d = 1) Beta(d = 2) Beta(d = 3)
#> 1 1.560185339 2.436736880 9.3759254766
#> X^1 0.031757430 -0.013118656 0.0022353338
#> X^2 -0.029246827 0.014785102 -0.0029660706
#> X^3 0.006817707 -0.003720884 0.0007588487
#>
#> Covariance matrix:
#>
#> 3.804381e-04 -6.347547e-05 1.145850e-05
#> -6.347547e-05 1.518183e-04 -2.400721e-05
#> 1.145850e-05 -2.400721e-05 7.131206e-05
#> -----------------
#> Regime 2 (k = 2):
#>
#> Regression coefficients:
#>
#> Beta(d = 1) Beta(d = 2) Beta(d = 3)
#> 1 152.876126 -51.6307852 -101.7640938
#> X^1 -99.280212 33.0383816 68.3336097
#> X^2 20.838377 -6.4071123 -13.2834754
#> X^3 -1.376692 0.3927075 0.7941306
#>
#> Covariance matrix:
#>
#> 0.234496465 0.01028499 0.003237261
#> 0.010284994 0.17150241 0.034012464
#> 0.003237261 0.03401246 0.173280983
#> -----------------
#> Regime 3 (k = 3):
#>
#> Regression coefficients:
#>
#> Beta(d = 1) Beta(d = 2) Beta(d = 3)
#> 1 10.2836153396 5.850804e-01 1.553479606
#> X^1 -0.1473590788 -1.117067e-01 -0.837211380
#> X^2 0.0102792674 6.430785e-03 0.068044546
#> X^3 -0.0002175552 -8.980275e-05 -0.001859245
#>
#> Covariance matrix:
#>
#> 0.0006488799 -1.218436e-04 1.883261e-04
#> -0.0001218436 1.380695e-03 -7.025104e-05
#> 0.0001883261 -7.025104e-05 2.431844e-03
#> -----------------
#> Regime 4 (k = 4):
#>
#> Regression coefficients:
#>
#> Beta(d = 1) Beta(d = 2) Beta(d = 3)
#> 1 -1029.8101854 334.7531623 466.4950948
#> X^1 199.9337269 -68.7757987 -105.7225685
#> X^2 -12.6537117 4.6522956 7.6607709
#> X^3 0.2626711 -0.1032888 -0.1778595
#>
#> Covariance matrix:
#>
#> 0.058681324 -0.017669792 0.002130003
#> -0.017669792 0.047589263 0.007854147
#> 0.002130003 0.007854147 0.067134426
#> -----------------
#> Regime 5 (k = 5):
#>
#> Regression coefficients:
#>
#> Beta(d = 1) Beta(d = 2) Beta(d = 3)
#> 1 26.839286686 -14.419457932 19.760634802
#> X^1 -3.470505723 2.286275938 -1.514079293
#> X^2 0.158288202 -0.101799143 0.073143231
#> X^3 -0.002398072 0.001493312 -0.001173409
#>
#> Covariance matrix:
#>
#> 0.0069094075 -0.0011760419 0.0000291898
#> -0.0011760419 0.0035957112 -0.0002395346
#> 0.0000291898 -0.0002395346 0.0005572795
mpwr$plot()
